The Geometry of Model Uncertainty

The over-confidence in mathematical models and the failure to account for model uncertainty have frequently been blamed for their infamous role in financial crises. Serious consideration of model ambiguity is vital not only in the financial industry and for proficient regulation but also for university level teaching.

Remarkably, it remains an open challenge to quantify the effects of model uncertainty in a coherent way. From a mathematical perspective, this is a delicate issue which touches on deep classical problems of stochastic analysis. In recent work, we establish a new link to the field of optimal transport. This yields a powerful geometric approach to the problem of model uncertainty and, more generally, the theory of stochastic processes.